Devi Aparadha Kshamapana Stotram was composed by Adi Shankaracharya.It is usually customary to recite the stotram after the completion of a Chandi Patha recital or after the completion of any Devi Puja.
It is like asking for forgiveness from Mother Goddess for the various offences(like not uttering Mantras correctly,not showing Mudras properly or even general offences) one might have committed during the recital/puja(or otherwise).
The theme of this Storam is of total surrender to Mother Goddess and asking Her for forgiveness. Just like a mother never abandons her son ,no matter how many mistakes he might have committed,similarly this stotram asks Goddess to protect & forgive us like Her son.
The benefits of reciting(honestly) the stotram is obviously getting forgiven by Mother Goddess of the offences and sins one has committed.
The Stotram has 12 verses in all ,few are given below(with meaning).
A similar Aparadha Kshamapana Stotram dedicated to Lord Shiva is this
न मत्रं नो यन्त्रं तदपि च न जाने स्तुतिमहो न चाह्वानं ध्यानं तदपि च न
जाने स्तुतिकथाः । न जाने मुद्रास्ते तदपि च न जाने विलपनं परं जाने
मातस्त्वदनुसरणं क्लेशहरणम् ॥१॥
(O mother neither i know your Mantra,our Yantra,your Stuti,your
Dhyanam,or even your Mudras.Not even i know how to cry for
you.However, one thing I know (for certain); By following You (somehow
through rememberance however imperfectly) will take away all my
Afflictions (from my Mind),
नाराधितासि विधिना विविधोपचारैः किं रुक्षचिन्तनपरैर्न कृतं वचोभिः ।
श्यामे त्वमेव यदि किञ्चन मय्यनाथे धत्से कृपामुचितमम्ब परं तवैव ॥९॥
(O Mother) I have not worshipped You as prescribed by tradition with
various rituals, (On the other hand) What rough thoughts did my mind
not think and my speech utter? O Shyama, inspite of this, if You
indeed, to a little extent, to this orphan ... ... have extended Your
Grace, O Supreme Mother, It indeed only becomes You (i.e. is possible
आपत्सु मग्नः स्मरणं त्वदीयं करोमि दुर्गे करुणार्णवेशि । नैतच्छठत्वं मम
भावयेथाः क्षुधातृषार्ता जननीं स्मरन्ति ॥१०॥
(O Mother) I have sunk in Misfortunes and therefore remembering You
now (which I never did before), O Mother Durga, (You Who are) an
Ocean of Compassion, ... ... (Therefore) do not think of me as false
(and my invocation as pretence), (Because) When children are
afflicted with Hunger and Thirst, they naturally remember their Mother
मत्समः पातकी नास्ति पापघ्नी त्वत्समा न हि । एवं ज्ञात्वा महादेवि
यथायोग्यं तथा कुरु ॥१२॥
(O Mother) There is no one as Fallen like me, and there is no one as
Uplifting ( by removing Sins ) like You, Considering thus, O
Mahadevi, Please do whatever is proper (to save me).