Translation:Although he is rich, he is not happy.
A useful rule for word order in German is that (in normal sentences) the (conjugated) verb must be in the second position. Note that the second position does not necessarily mean the second word - certain constructions like subclauses are considered as a whole to occupy one 'position', and there are even some words which go in 'position 0'! But using this rule, I'll show you how it helps form this sentence.
At its simplest, this sentence could be Er ist nicht glücklich. We see here that the subject (the nominative bit) is er, and the verb is ist. Note that the verb conjugates to match the subject, as always. This simple sentence only has one verb so that's pretty easy. The verb is in the second position, also the second word. Totally normal sentence (German: Hauptsatz). Easy peasy.
[Er] [ist] [nicht glücklich]
[position 1] [position 2] [...]
[subject] [verb] [everything else]
Now we want to add extra information to the sentence (German likes doing this a lot). This information is "although he is rich". In German as in English, this information alone is not a complete sentence - it's a subclause (German: Nebensatz). This means we can't just write it as a separate sentence with a full-stop between - it needs to be added into the main sentence somehow, as one unbroken unit. German does this by using commas to separate the subclause from the main sentence, which helps us identify it more easily. Here, the subclause has been put in the first position, which pushes out er to be after the verb - because ist still needs to be in the 'second position':
More complicated sentence:
[Obwohl er reich ist], [ist] [er] [nicht glücklich]
[position 1], [position 2] [position 3] [...]
[subclause], [verb] [subject] [everything else]
Is that clear enough?
It might seem strange that the subject can get pushed around like that (it's a pretty important part of the sentence!), but in German it's totally possible because it usually uniquely conjugates the verb. Moving it around can change the emphasis a bit though, so try not to go too crazy until you get a feeling for it. As an example, Ich spiele gern Fußball is quite neutral with emphasis but Fußball spiele ich gern emphasises that it's football that I like to play. Note that in both sentences the verb stays fixed in second place, and conjugates to the subject ich just the same.
We can actually put the subclause at the end instead of the start (to play with the emphasis or flow of the sentence). This would allow the subject to remain at the front, and might look a bit more 'normal' to you: Er ist nicht glücklich, obwohl er reich ist. The subclause remains together as before, and is separated from the main sentence by a comma. (Although it sounds very strange with this specific example, you could also put the subclause in the middle for special emphasis, with commas on both sides: Er ist, obwohl er reich ist, nicht glücklich.)
The subclause itself uses a different word order, with the conjugated verb at the end. This is very common for subclauses. Subclauses are often formed because of a special 'trigger' word called a conjunction. These are the words that combine together multiple pieces of information: "although", "but", "because", "during", "after", etc. Many of these conjunctions are subordinating conjunctions, meaning they require a subclause with the verb at the end. Obwohl is one of these. As a normal sentence, that information would be Er ist reich, but when you put it into a subclause (Nebensatz), the ist gets pushed to the end: Obwohl er reich ist. Remember that this needs to be added as one element into a main sentence though - it's not complete by itself.
This is a tricky point of German word order, so let me explain as simply as I can. "Obwohl" is okay of a group of conjunctions that also includes "wenn", "ob", "als" and "weil". These conjunctions can be used in two ways. Firstly, they can be used in the middle of a sentence, where they put the main verb to the end: "Ich kann nicht einkaufen gehen, wenn ich kein Geld habe". Secondly, they can be used at the start of a sentence, where they put the verb to the end of the first part (before the comma), and the main verb of the second part follows immediately after the comma: "Wenn ich kein Geld habe, kann ich nicht einkaufen gehen"