Learn Hardcore Swedish: Bränningen tar lång tid.

So the sentence uses the definite form, not the basic dictionary form. Swedish often marks the by adding an ending to the noun instead of using a separate word.

What kind of word is bränningen?

It is a noun. The base form is bränning, and in many contexts it is related to the verb bränna. In Swedish, nouns like this are often formed from verbs and describe a process, event, or result.

The exact English translation depends on context, but grammatically it behaves like an ordinary singular noun here.

What does tar mean here?

Here tar is the present tense of ta, and it means takes.

Swedish very commonly uses ta in time expressions:

Det tar tid = It takes time
Det tar lång tid = It takes a long time
Bränningen tar lång tid = The burning/firing/etc. takes a long time

So this is a very normal Swedish pattern.