In our life we accumulate many things like memories, beliefs, knowledge, etc.
But after death what do we actually carry from current life into afterlife, and what things will fill the next body after rebirth?
The 5 senses along with mind as the 6th (head of other 5) are carried to the afterlife or next birth, when the physical body dies.
BG 15.7 -- Among the living world, the living being (bhuta = body) is my eternal fragment only; It (fragment or body) keeps attracting 5 senses & mind as the 6th towards the material nature.
BG 15.8 -- When the Body is received and also when given up, the "Master" (ishvara = master, here) carries all these [6 senses]; Same as wind transporting smell.
BG 15.9 -- Residing over [senses of] 'hearing, eyes, touch, taste and smell and also the mind', "That" consumes/enjoys [various] subjects.
So you may ask, what is 'we' in your Q?
"... what do "we" carry into afterlife ...?"
It boils down to "what do 'I' carry into afterlife".
Now until this 'I' is individual, it's termed as "Purusha" (consciousness), the enjoyer or consumer of various happiness & sorrow & emotions of life. There are numerous verses suggesting that this Purusha is in turn the part of Atma# or the supreme true self only. However, the Purusha interacts with the material nature (Prakruti), the Atma doesn't.
The double quotes mentioned in above verses as "Master" & "That" is "Purusha" only. To answer your Q:
The Purusha carries 'mind + senses' to theafterlife or the next birth.
Q: For what purpose Purushas (we) keep travelling from body to body?
A: To enjoy various aspects of material nature (Prakruti).
Q: Why "enjoy" sorrow & pain?
A: Any emotion is enjoyable for Purusha. Compare it with watching a film!
This "enjoyer" (Ananda Sharira) term creates confusion for many. During Gita, Krishna has used other terms also to suit different people's tastes: "Consumer" (Bhokta) & "Witness" (Upadrushta).
Q: Until what time, this so called "enjoyment" continues?
A: Until the Purusha is not completely "bored" of nature & it's purposes. Once it's convinced that in all facets of life from top to bottom, there is only reasons of misery (BG 8.15,16), it automatically starts giving up. It doesn't differentiate anymore between opposites. In other words, the "dualities" begin to perish. Neither good nor bad, neither right nor wrong, neither support nor oppose, ... neither this nor that.
Q: And then ...?
A: Finally Purusha disappears, hence nothing remains to reborn. This is also called merging with Atma or Moksha/NirvAna or liberation.
Q: Does this "non-differentiating" attitude or path to liberation manifest in a person's actions?
A: No. Physical actions has nothing to do with the person's path of liberation. On face value a person may appear very sinful, but still he/she can be on way to liberation compared to a person appearing pious.
See this answer. Besides that, there are few verses which support it. Like "knowers also act as per their material nature" & "an extremely sinful person should be considered as saint when his/her consciousness is fixed on Me/Atma".
Q: Any other aspect, which represents "Purusha"?
A: According to SAmkhya, Buddhi/intellect is born out of the interaction between Purusha + Prakruti. So Buddhi, which resides between mind (Mann) & supreme self (Atma) is the closest objectification of Purusha.
BG 3.42 — Indriya-s/senses are said to be beyond [physical body]; Mann/mind is beyond senses; Buddhi/intellect is even beyond Mind; "That" (Atma) is even beyond intellect.
# - Some people differentiate between Atma & ParamAtma, they might be right in certain context. But actually there is no difference between these terms. It's as good as "Krishna" vs "Shri Krishna" or "Jesus" vs "Lord Jesus". ParamAtma is typically useful, when Atma is used in context of "false ego". But once the "false" is cleared, both Atma & ParamAtma are same.
To our next life we do not carry memories and knowledge, but rather our affinities (a spontaneous or natural liking or sympathy for something) and desires, ie something that we like, and interest for something that we developed in this life. We also carry some knowledge to the next life, but it will stay to be deeply dormant in our consciousness and thus we can't remember it exactly in the next life but it can help us to easily learn new things that are of the same type of knowledge like we had in the previous life.
Thus if you were interested in the pursuit of spiritual knowledge in this life, you can easily continue your interest for the same in the next life. We have a confirmation of that in the teachings of Lord Krishna in the Bhagavad gita 6.43-45, see at http://www.vedabase.com/en/bg/6
"On taking such a birth, he revives the divine consciousness of his previous life, and he again tries to make further progress ..."
I have explained that in the related question at Do people have same preferences and liking towards everything in this world or are they wiped like a clean slate after reincarnation?
Thus we can say that we do carry our affinities, and in some sense even knowledge (in deeply dormant state) to our next life.
All those things that we carry with us to our next life we have shaped with our deeds (karma) and our desires. Of course our karma that we have to enjoy and suffer we also take with us to the next life.
Similarly to the above quotation from the Bhagavad gita it is said in the Smriti scripture called the Suśruta-saṃhitā, an ancient Sanskrit text on Ayurveda medicine: https://en.wikipedia.org/wiki/Sushruta_Samhita
Sushruta-samhita, book Sarira-sthana, chapter 2, verses 54-55, page 133: https://archive.org/stream/englishtranslati00susruoft#page/132/mode/2up
"Acts similar to those, which a man performs in a prior existence, overtake him also in the next. Similarly the traits and the temperament which he had developed in a previous existence are likewise sure to be patent in the next."
Thus the Sushruta-samhita says that a man will be interested to perform the acts of the same kind or in some sense similar to those acts that he performed in his past life, and even the traits of his personality and the temperament which he had developed in his past life will continue to be easily recognizable.