As a particle, が has several different uses in Japanese. However, each of these different uses share a common theme. That theme expresses ‘highlighting (A) as important, (B)’. In this use, が comes across as ‘but’, or ‘however’ in English.
This nuance of が is used directly after any form of verb or い-Adjective, but requires one of the conjugations of だ or です before it when used with a noun or な-Adjective.

• 毎日（まいにち）走（はし）るが、運動（うんどう）はきらい。
  I run everyday, but I don't like exercise.
• このカレーは辛（から）いが、美味（おい）しい。
  This curry is spicy, but delicious.
• 車（くるま）は便利（べんり）だが、危（あぶ）ない。
  Cars are convenient, but dangerous.
• お金（かね）は大切（たいせつ）だが、時間（じかん）も大切（たいせつ）だ。
  Money is important, but time is also important.

From these examples, we can see that が is simply highlighting that ‘while (A) is important, there is extra information’. が with the meaning of ‘but’ is considered to be very formal, this is due to it sounding quite direct in asserting that there is extra information.