One of those max. 4 primary partitions can be an extended partition which in turn can hold up to 16 logical partitions. So in total you can create up to 19 usable partitions on a drive with an MBR partition table.

If you choose “something else“ as installation type, the partition manager of the Ubuntu installer lets you choose between creating primary or logical partitions:

The partition manager will automatically create an extended partition if necessary to accommodate a newly created logical partition. It hides the complexity of dealing with this technical detail.

You should not forgo swap space:

• If your computer runs out of physical main memory and has no swap space to fall back on, it will

  
  
  
  
  
  • start to kill user space processes¹ (and it's hard to predict which ones) to accommodate memory needs of the kernel and
  
  
  • behave erratically, because memory allocation for user space processes¹ will fail, which most applications aren't programmed to anticipate; this usually leads to crashes because these applications then try to access invalid memory addresses.
  
  



• While it's possible to have a swap file inside a file system, suspension to a swap file isn't implemented in the kernel. You pretty much need a swap partition for that.




• As I described above it's easy enough to create a swap partition if you can have up to 19 partitions on one drive – a big deal easier than dealing with the aforementioned two problems.

See also https://help.ubuntu.com/community/DualBoot/Partitions

¹ A “user space process“ is what a layman may call an “application”, but the former also encompass other things like server applications and system services.