How is an exoplanet characterised as "Earth-Like"? Which features or characteristics are taken into account to characterize an exoplanet as "Earth-Like"?
There is no unique definition of Earth-like and it depends on what characteristics are important in the context of discussion.

The most simple one is to just compare radii and masses. That is observationally sensible as radius is directly deducable from transits (assuming stellar size known) and mass is often an accessible properties for transiting planets when you have access to complementary radial-velocity data. It's also a good starting point if you want to add  further restrictions. The habitable planet catalogue uses this definition (considering only planets in the habitable zones around their stars, using a simple equilibrium temperature definition)

If your quest is actually for a 2nd Earth not only in surface gravity but other characteristics, one approach is outlined by the Earth similarity index (ESI). While it is not directly a measure for habitability either, it is a good proxy by comparing more essential parameters with Earth like mass, gravity, surface temperature. For a selection of parameters you define this ESI as 

$$
\mathrm{ESI} = \prod_{i=1}^n \left(1 - \frac{x_i - x_{i,o}}{x_i + x_{i,o} }\right)^{w_i/n}
$$

where $ x_{i,o} $ is the Earth's value of a property and $n$ the total number of properties. This is basically a weighted geometric mean of the property differences. It is a good idea to consider 'internal values' and 'external' ones. The Planetary Habitability Lab uses surface temperature and escape velocity as external and radius and density as internal and use this to create a nice 2D scatter plot for known planets.