Example sentences
xiǎng想qù去，dàn但shì是méi没shí时jiān间。
Want to go, but no time.
hǎo好shì是hǎo好，dàn但shì是guì贵。
It's good, but expensive.
About this word
但 is an old word meaning only or merely, and 是 is the verb to be, so 但是 is literally "it is only that". The phrase first introduced a qualification, and that is precisely the work but does in English. 但 on its own is now a common short substitute, especially in writing. In speech 但是 sounds slightly formal, while 可是 and 不过 are lighter, with 不过 the softest of the three. It always opens the second clause, never the first.
The story behind the character
但
但 is 亻 (person) plus 旦, which carries the sound. Xu Shen wrote 但, 裼也: to bare the upper body, to strip to the waist. Nothing about contrast or turning a sentence around. It got borrowed for the word "but" somewhere along the way and never gave the body meaning back. So when you write 但是, you are using a character that once meant taking your shirt off.
是
日 (sun) over 正 (straight). Xu Shen wrote 是, 直也: "to be straight." The sun at high noon, dead center, not leaning. That was 是. It only later became the verb "to be." So 是 started as "straight," not "is."