Lequel (and its forms laquelle, lesquels, lesquelles) replaces a noun after a preposition other than de, when qui alone would be ambiguous or when the antecedent is a thing rather than a person: le stylo avec lequel j'écris (the pen with which I write), la raison pour laquelle je pars (the reason why I'm leaving).
Lequel contracts with à and de the same way le does: à + lequel becomes auquel, de + lequel becomes duquel. For people, avec qui is generally preferred over avec lequel (l'ami avec qui je voyage), but lequel is required for things and is the only option after most other prepositions when referring to an object.