This question is asked often in Ask Ubuntu, sometimes with few hints about the situation.
Please provide a list of possible reasons to help troubleshoot the problem.
Three more reasons not on the original list:
Bad USB flash drive. This could even be a new flash drive which I assume to be not corrupted. Ubuntu will boot after making the Ubuntu live USB on a different USB flash drive. It's worth a try if you have two or more USB flash drives.
Reformat the flash drive and reload the Ubuntu ISO from an application for making a live USB.
Voltage irregularities that affect the smooth amount of voltage delivered from the motherboard to the USB flash drive. Possible causes of this are motherboard, power supply and even irregular house current. A very old computer is more likely than a new computer to have issues with the motherboard or power supply that affect booting to a live USB session. Believe it or not the Ubuntu live USB will sometimes be able to boot if the same computer is moved to another location that has a more controlled source of current.
Some applications for making Ubuntu live USBs seem to work better than others. For example, the built-in Startup Disk Creator application is better than most.
There are many reasons a persistent USB might not boot.
USB not set as first hard drive in BIOS
Problems with BIOS or UEFI boot partitions or files.
Secure Boot is not turned off
Drive not compatible with computers BIOS or UEFI boot mode
Incorrect partition table
Out of date BIOS/UEFI firmware
Junk in volatile memory
Incorrect root partition in grub
Incorrect path to ISO in grub
Incorrect persistent-path, (if used), in grub
Grub menu entry structure not suiting OS
Incorrect file type for vmlinuz and initrd (.efi and .lz)
The word "persistent" is missing from grub.cfg, txt.cfg, syslinux.cfg or text.cfg
Persistence (casper-rw and home-rw)
Persistence partition is not an ext filesystem
Persistence file not on FAT filesystem
Persistence file/partition reused from different version
Persistence file full of data, or file update attempted
Corrupted flash drive, reformat and reload
Bad flash drive
Not enough RAM to run Ubuntu
Bad or incorrect USB socket
Incompatible computer CPU
Incompatible computer GPU
Computer does not meet minimum specs, a lighter version of 'buntu is required
Motherboard voltage irregularities
Motherboard BIOS limitation with multiple USB devices
Bad MD5SUM / corrupt ISO file
Modified or corrupted ISO9660 partition
USB was removed from computer before ISO file is completely copied
Out of date boot drive creation tool
User inexperienced with boot procedure
Thanks to karel and sudodus for help with the answer. See Why Doesn't my Bootable USB Boot
Great idea to create a list and a flowchart for this subject :-)
I would like to add
the user does not know how to get to a temporary boot menu and how to get into the UEFI/BIOS menu system to modify the settings, should be possible to help when the computer brand name and model are known
secure boot might prohibit USB boot in general or a boot drive made without completely signed software, should be possible to turn off secure boot
mini.iso, which boots only in BIOS mode