Flaps are used for safe TakeOff and landing on fast aircraft. TakeOff without flaps could be possible, but a longer runway would be required to gather the extra speed. Landing without flaps means a prohibitively high landing speed.
Lift and drag on aeroplanes aree proportional to wing area S, wing profile curvature $C_L$, air density $\rho$, and airspeed squared, the well know lift and drag equations:
$$L = C_L \cdot \frac{1}{2} \rho V^2 \cdot S$$
$$D = C_D \cdot \frac{1}{2} \rho V^2 \cdot S$$
At high airspeed, the lift required can be produced by a relatively small wing area, which then also reduces drag so that less fuel is used for the trip. But with a relatively small wing area, flying slow can become an issue. To maintain enough lift to keep the plane up, the $C_L$ needs to be increased by flying with the nose up, and this has a limit beyond which the wing stalls and the plane will sink.

Flaps increase $ C_L$. The graph above was earlier used in this answer and shows how $C_L$ is increased at every angle of attack. At TakeOff flaps are used (partly deployed) on faster planes, but they are particularly important durimg landing when they are deployed fully. Fast jets often have Fowler flaps, which increase both the $C_L$ and the wing area.