Why gap is maintained between the rails of railway track?

This would be the problem if gaps are not maintained between the rails.

All solids expand (increase in size) in a certain measure when subjected to high temperatures — and contract when cooled. This is a basic thermodynamic fact: molecules always vibrate and when heated, this vibration increases, slightly expanding the bulk of the material. When the main dimension of a solid is linear (like in rails) we talk of linear thermal expansion. This effect can be modeled with a constant coefficient for ambient temperatures. Rails are made of a steel which has a linear thermal expansion coefficient of around 12 µm/(m·K). That is: each meter of rail expands 0,012 millimeters for each degree of temperature increase (Kelvin and Centigrade are the same “size”, and being a relative measure it does not matter which one we consider).

In practical terms: let’s assume we are using 90 m rails at 15 °C. What will be the rail length in a hot, 40 °C summer day? Computing 12 × 90 × (40 – 15) gives 27000 µm, that is, a whopping 2.7 cm which must be accounted for when laying down tracks, lest rails expand beyond the dilation clearance and start pushing against one another, risking sag and perhaps a derailment. Dilation clearances between rails are best calculated for the most usual temperature at the locale.

Modern railways employ continuous soldered rails and track expansion devices at regular intervals (and usually at the start and end of bridges, tunnels and other structures) to avoid the maintenance problems posed by rail thermal expansion and to increase rolling comfort.