Trim marks, tick marks or crop marks
Most printing is done on larger sized paper. So A4 leaflets might be printed '2 to view' on SRA3 paper and cut down to A4. Crop marks or 'crops' show the guillotine operator where to trim the sheet. Most professional programmes (and Publisher!) allow you to add crops to your work. And yes, you need crop marks even if you don't have bleed so that your job can be cut to the correct size. Always include crop marks if you can.
Bleed
When you bleed a document, that is, extend an item off the edge of the page it goes a 'bleed' area. Bleed is important. If you don't add 'bleed' and the object stops at the edge of the paper, when the guillotine blade trims/crops close to the object it could miss by a sliver - then you would have a sliver of white on the printed piece - highly undesirable. Bleed should be 3mm on each edge. Take a look at the pictures to see what you should be doing.