A language learned by a person after his or her native language, esp. as a resident of an area where it is in general use. (http://www.thefreedictionary.com/second+language)
A second language is a language that is learned in addition to a person's mother tongue, or first language. English is the second language learned by most people worldwide. These languages may be acquired by absorption, because it is spoken in the home, or actively pursued by taking courses. The more the language differs from a person's mother tongue in terms of alphabet and grammar, the more difficult it will be to learn. Modern technology, however, provides many resources to make the process easier and more fun. (http://www.wisegeek.org/what-is-a-second-language.htm)
Children can typically learn a second language much more easily than can adults, although there is no reason the latter cannot reach a proficient level in whichever language they wish to learn. Having a second — or third or fourth — language can be of great benefit when it comes to international business and travel. Learning a new language has also been associated with better reading ability in the mother tongue, improved test scores, and better performance at a college level, as it seems that the process improves thinking skills in general. (ibid)
Second language acquisition, or SLA, has two meanings. In a general sense it is a term to describe learning a second language. More specifically, it is the name of the theory of the process by which we acquire - or pick up - a second language. This is mainly a subconscious process which happens while we focus on communication. It can be compared with second language learning, which describes how formal language education helps us learn language through more conscious processes. For example
a learner studying in an English-speaking country may have more success due to the language they acquire in their part-time job than with the language they learn in their class. (http://www.teachingenglish.org.uk/knowledge-database/second-language-acquisition-sla)