I recently read somewhere that there are some countries in the world are actually larger than they are shown on the world map. For eg. Somalia is significantly larger than it is shown on the map and Congo is almost as the same size as India. Is this true ? Are they just shown smaller due to some calculations related to projections or are they actually larger in size and there is some geopolitics behind it ?
The Earth is round, and it is not possible to project a flat map such that all countries retain the same area as they originally are. If this influences your political thinking, use a globe.
Commonly countries close to the North and South poles are depicted larger. Especially Greenland is depicted almost as big as Australia that is actually not true.
The relative size of countries also depends on the chosen projection of the map, so it may be possible to use it for subtle propaganda, by systematically using some projection with known distortions.
The USA even has the specialized GS50 projection to show all its states with as little distortion as possible. It is a complex projection, produced using high order polynomials.
It's just because the earth is a sphere being transformed onto a rectangular view using the Mercator Projection. With this projection, countries near the poles seem a lot larger than they actually are.
This is a geographical, not really a political question
Are they just shown smaller due to some calculations related to projections or are they actually larger in size and there is some geopolitics behind it ?
Most world-maps we see use the Mercator projection. This was initially popular because it had properties that were extremely useful to ship's navigators in the age of wooden sailing ships (and beyond). In particular I believe a straight line on a Mercator map corresponds closely to a constant compass course (if we ignore magnetic anomalies, declination etc) - So a navigator can use a ruler to draw a line to a destination port and use a protractor to read the direction the helmsman should steer (after adjusting for currents, wind etc).
This usefulness led to the popularity of this particular projection.
Nowadays it's use is generally unjustified and for most purposes there are better projections we should be using instead. Most of these other projections provide a much better indication of the comparative size of countries.
In the age of computers and GPS, most of us no longer need a map whose primary usefulness is for plotting courses with pencils, protractors and magnetic compasses.