As you perform inserts updates and deletes, your indexes will become fragmented both internally and externally.
Internal fragmentation is you have a high percentage of free space on your index pages, meaning that SQL Server needs to read more pages when scanning the index.
External fragmentation is when the pages of the index are not in order any more, so SQL Server has to do more work, especially in IO terms to read the index.
If your indexes become too fragmented, at best, your queries will be less efficient but at worst, SQL Server will just stop using the indexes all together, meaning virtually all queries would have to perform a table scan or clustered index scan. This will hurt your performance a lot!
When you reorganise an index, then SQL Server uses the existing index pages and just shuffles data around on those ages. This will alleviate internal fragmentation and can also remove a small amount of external fragmentation. It is a lighter weight operation than rebuild and is always online.
When you rebuild an index, SQL Server actually resorts the data of the index and uses a new set of index pages. This will obviously alleviate both internal and external fragmentation but is a more heavy weight operation and by default causes the index to go offline, although it can be performed as an online operation, depending on your SQL Server version and settings.
Please do not expect to have 0 fragmentation after a Rebuild however. Unless you use a MAXDOP query hint, SQL Server will parallelise the rebuild operation and the more processors involved, the more fragmentation there is likely to be, because each processor or core, will rebuild their section or fragment of the index individually, without regard for each other. This is a trade off between best fragmentation levels and time taken to rebuild the index. For near 0 fragmentation, use MAXDOP 1 and sort the results in TempDB.
Instead of looking at indexes, start looking at what queries are causing the high CPU use. Start with Michael J. Swart's DMV queries to find the top CPU-using queries. Look at what indexes the queries are using, whether they're doing things like implicit conversion, etc. But generally no, fragmentation by itself probably isn't doing this.
Best Answer
The SQL Server will maintain these indexes automatically. If they have become fragmented you'll need to defragment them manually or via a scheduled job just like the user databases.