First of all, it should be noted that the Sri Sukta is a Khila Sukta of the Rig Veda, meaning that it's a hymn found in the Bashkala Shakha or recession of the Rig Veda Samhita, but it's not found in the Shakala Shakha of the Rig Veda Samhita. (See my answer here for more information on the Vedic Shakhas, and my answer here for information on the different parts of the Vedas.)
In any case, here is what this excerpt from the Brihaddevata, an ancient work by the sage Shaunaka, says about the Sri Sukta:
But the hymn of Fortune (śrīsūkta) is a benediction.
So the Sri Sukta is a hymn that gives you blessings. For more detail we can turn to the Lakshmi Tantra, a Pancharatra text which takes the form of a dialogue between Lakshmi and Indra. (For more information on the Pancharatra texts, see my answer here.).
In this chapter of the Lakshmi Tantra, Lakshmi tells Indra about the glories of the Sri Sukta. Here is the origin of the Sri Sukta:
In order to be merciful towards the worlds and benefit living beings, this pair of us, the ultimate parents of the world dwelling in infinite space with divine majesty (parayā śriyā), once (thought) out of compassion 'how can these creatures be happy and united with us?' While searching for a solution in profound concentration that (pair of us) churned (as it were) the vast, deep ocean of Śabdabrahman. When churned, out of that (Śabdabrahman) containing Rg, Saman and Yajus, emerged the divine twin suktas, in the same way as butter comes out of (churned) thick milk. The pair (of sūktas) is integral (anāhata), unambiguous, clear, undecaying, containing all majesty and attributes and possessed of flawless syllables and words.
So Vishnu and Lakshmi, out of compassion for Jivas, "churned" out of the Vedas two hymns, the Purusha Sukta and the Sri Sukta. In any case, here is the preamble to the Sri Sukta:
I myself am regarded as its seer, its metre is said to be Sri. I, the wife of Visnu and the Goddess containing everything, am its deity. It is used for the worship of Lakshmi and Narayana.
And here are the Dhyana shlokas (which I discuss here) of the Sri Sukta:
(The adept) should visualize me, the noble Goddess Laksmi, as seated on Visnu's lap, perpetually embraced by the Supreme Self with His left arm (encircling) me while (one of) my lotus carry arms rests on His shoulder.
Then a detailed procedure is given for chanting the Sri Suktam. You can read the details in the chapter, but in part it involves the chanting of each name or Lakshmi in a separate mantra, similar to what is done for the Vishnu Sahasranamam. Also, various stories of people worshipping Lakshmi using these mantras and the benefits they received are given, for instance ths story of Shiva I discuss here.
Then the general benefits of chanting the Sri Suktam are described:
O Sakra, the greatest eradicator of all evil and the remover of all bad luck (alakshmi), this my sukta should be recited on the occasion of any religious rite. It strengthens the power of ritual acts, brings prosperity to the listener, destroys all delusion and removes all bad fortune as well as imperfections. When (an adept) worships it employing physical, mental, and verbal functions, it saves him from heinous sins and bestows everlasting prosperity on him.
By the way, on a side note I posted a question here about the "sons" of Lakshmi, who are also considered to be the seers of the Sri Sukta.