。
She came over here to talk with me.
Literal
She [topic-は] me [with-と] talk do [purpose-に] this-direction [to-へ] came.
The purpose-marking に attaches to a verb stem (話をしに) and combines with a motion verb (来る) to express 'came in order to do X.' This is one of the most common purpose constructions in Japanese — verb-stem + に + motion verb. 話をする is a 'light verb construction' where する takes the noun 話 ('a talk, a conversation') as its object: 'to do a talk' = to talk. こちら literally means 'this way / this side' and politely substitutes for ここ ('here'); using こちら subtly elevates the listener or sets a more polite tone.