Note: I am sure SuperUser already has a good answer on this. I couldn't find it, however.)
Both disks and filesystems divide their space in blocks (sectors, clusters) of a certain size, normally multiples of two in the range 512 B ~ 8192 B.
When a partition is not "aligned" – that is, when a filesystem starts in the middle of a physical sector – writing a single filesystem cluster involves reading, updating, and then rewriting multiple physical sectors:
1 2 3
1 2 3 4
In the example above, writing filesystem cluster #2 would require the disk controller to read blocks #2 and #3, then write back to the same location (after waiting for the platters to spin almost 360° if it's a hard disk).
But if the partition is aligned, all that's needed is a single write.
Recent high-capacity disks use 4096 B sectors physically (called "Advanced Format"), but the OS sees each sector as 8 sectors 512 B each. Even if the filesystem is aligned to those 512 B sectors, it might still start in the middle of a real 4 kiB sector, resulting in the same problem as above.
To avoid this and related alignment problems in the future, many partitioning programs have started aligning at boundaries as high as 1 MiB (which isn't that much of a loss on terabyte disks anyway).