The Illustrator join tool is found beneath the shaper tool in the toolbar and is for combining paths and trimming paths / lines / open paths etc. It works using two lines either selected or not (though personally, I generally select the paths I use and then use the tool with the paths). Select two open paths such as two lines and then Go to the tool in the toolbar and Pass over the closest ends of the two paths
If there is a fairly major overlap with the paths, you may find the join fails and instead you will trim the paths. The join tool is very dependent on where you pass over the paths. If you use it with a path overlapping another, and you use the join close to the overlap then the paths will be trimmed. The same paths can also be joined if you pass it over the end segments. This is particularly the case with multiple point paths or curved paths created with the curvature tool. It also depends where the pass over happens, if the overlap is a fair distance away then the lines will not be trimmed (again this is just an observation and I am certain you will find circumstances where the opposite happens)
You can see two lines with both lines point towards each other at one end and the other ends heading off to eternity. You can use the join tool over the ends that are angled towards each other. There is a cut off point where the angle is too great for the tool to process the paths and in that case, the join will fail. You can angle the line so they are close to parallel and the tool will not work, you can then angle them at say about 80 degrees so they are fairly parallel and the join tool will not work but at some point where the angles can be joined (without it flying off the page / art board etc) you will get a sharp join when you pass the two lines with the tool. Create a line using the line segment tool and then Create another line using the line segment. Place the lines close together. Point the ends of the lines towards each other. Select the tool in the toolbar. Draw over the end of the lines with the tool. if the paths are too far away then it will not work and it will not display a reason.
The trimming works if you have a line butting close to an existing line. The trimming works if the lines crossover. Again, the tool does depend on the distance of the lines from each other (too far away and the trimming will fail). The trimming is applied to the smallest part of the lines. If you can't trim the crossover lines, the tool just doesn't do anything - there is no dialog box with an error message (a rarity from an Adobe application). You can draw over a different part of the crossover and the action will be ignored. Create a line using the line segment tool. Create another line using the line segment tool. Rotate them and have the paths crossover. Select the tool in the toolbar. Draw over the smallest part of the crossover (the trailing parts of the lines) and the tool should then trim the lines and replace the two with one single sharp pointed line.
Instead of just straight lines, this can also work with curved lines but the tool does not create a curved combination (sadly) but again a sharp point will result. Click on the curvature tool. Create a curved path. De-select. Create another curved path using curvature tool or duplicate. Move the paths so the paths are not parallel but angled so the lines seem that they will combine at a point (not too far off point) and that the ends of the lines are fairly close (seems to work best). With this combination of paths you can apply the usual combination but if you pass the tool over the two top end points (or slightly further down as well) then that will combine. If you move over the overlap in the center or slightly below then a cut will happen. If you pass over the bottom points then nothing will happen. Of course, once you have combined the paths, you cannot re-use the tool again unless you select a second path. I am not sure how many paths can be combined or if there is a limit to the number of points etc.
You can use it to trim and combine brush strokes as well (they are just strokes with an attached brush stroke). The same resulting trim etc happens as explained above. Sometimes the actual brush stroke design may obscure the actual strokes making it a little less predictable.