Why do we need imaginary lines such as the equator? What is its purpose?

For navigation and geographic purposes. To identify location and distance.

The equator is not so imaginary as it is the part of the earth that determines the seasons in relation to the sun.

The equator is a very important planetary measurement tool:

https://en.wikipedia.org/wiki/Equator

Actually it is the Poles that determines seasons. The Earths axis, being offset, is what causes seasons. The Equator is just that, an equator.

e·quate

1. To make equal or equivalent.
2. To reduce to a standard or an average; equalize.
3. To consider, treat, or depict as equal or equivalent: equates inexperience with youth.

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E·qua·tor:
n.

1.
1. The imaginary great circle around the earth's surface, equidistant from the poles and perpendicular to the earth's axis of rotation. It divides the earth into the Northern Hemisphere and the Southern Hemisphere.
2. A similar great circle drawn on the surface of a celestial body at right angles to the axis of rotation.
2. The celestial equator.
3. A circle that divides a sphere or other surface into congruent parts.

At the Equator there exists comparatively no seasons because the equator is equidistant from the sun year-round (barring any eliptical perigeal or apogeal earth orbit factors)