DIAGNOSIS This is usually caused by food debris or congealed grease jamming the release mechanism on the basket handle, or the interior pan being warped from heat.
FIX 1) Let the fryer cool completely. Force will just make it worse. 2) Look at the black plastic handle. There's a silver button. Press it in firmly while simultaneously wiggling the basket from side to side as you pull. The wiggle is key. 3) If it's still stuck, unplug the unit. Use a butter knife or thin spatula to gently pry between the basket flange and the fryer body, applying pressure near the handle latch, not the middle.
IF THAT DIDN'T WORK The removable interior pan at the bottom might be warped upwards, physically blocking the basket. You'll need to reach in with long kitchen tongs or a hooked tool to try and pull that pan out first. Once it's out, the basket should release.
HEADS UP To prevent this, always make sure the interior pan and basket are clean and seated properly before cooking. A little food debris in the tracks is the most common culprit.