OK, so, the Aperture is a little hole (diaphragm) that allows certain amount of light reach the sensor. The unit used to measure the aperture is f/stops (written and numbers such as f/1.4 or f/8). The higher the number, the smaller the Aperture.
1) Aperture affects Depth of Field
This is the zone of sharpness in front of and behind of the focused point/object. Have you seen some photographs that the main object is sharp and focused but the background of the image is super blur? That is an example of narrow depth of field.
This is the relationship:
The lower the f/stop, the less depth of field and therefore the blurrier the background (because the opening is large).
And viceversa, the higher the f/stop, the more depth of field and the sharper the background (because the opening is smaller).
Here is an example of a low f/stop (f/2.8), look how blur the background is. That's is called bokeh
2) Aperture affects Shutter Speed
A low f/stop, for example f/2.8, means that the diaphragm (opening) is large, more light goes into the sensor, therefor less time is needed to take a picture (the shutter stays open for a shorter time). This means you can take quicker pictures (freezing the scene).