Lysosomes -Parts of the Cell

Lysosomes are small digestive vesicles found in a eukaryotic cell. Think of a vesicles as a heavy duty plastic bag. A lysosome is created at the Golgi apparatus.
The proteins of the lysosome are created at the rough ER and are packed in vesicles that are transported to the golgi apparatus. The golgi apparatus uses these proteins to make digestive enzymes and creates a vesicle that pinches off.
This vesicle is a lysosome
Lysosomes are found floating in the cytoplasm.

Please note, there is some debate about if lysosomes are found in plant cells. Most people feel the role of the lysosome is carried out by vacuoles in plants, some scientists feel that plants do have lysosomes.
Here is a short article that explains this briefly.

Vacuoles