The existing answers by Adam and Colin are sufficient, but I'd like to encourage you to consider the physics of trying to make the lines come "almost together".

If you are just studying this subject for the first time you may not yet have encountered all the concepts that follow. Don't worry about that, just put it on the back burner.

An exercise that might be instructive is to compute the electric field strength in a region where a +5 Volt and -5 Volt surface are brought very close together (say, 1 mm). How does that compare to the breakdown voltage of various materials. What if you reduce the separation to a 0.1 mm? To 0.01 mm? To a micrometer? The form of the answer is $$ E \propto \frac{V_2 - V_1}{d}$$ for $d$ the separation distance. Notice that the field strength would grow without bound if you allowed the separation to go to zero: always a sign that you're in dicey territory.

These issue become critical in the design of compact capacitors.

Electric fields also carry energy. So, how much energy per unit volume is required to maintain two different potential surfaces very close together? (You'll want to make some simplifying assumptions about the geometry if you're going to calculate exactly, or go go with the form of the equations. The form of the answer here is $$U \propto E^2 \propto \frac{(\Delta V)^2}{d^2}$$ which may be what was meant by causing problems related to energy if you try to make them come all the way together: this diverges even faster than before.

The existing answers by Adam and Colin are sufficient, but I'd like to encourage you to consider the physics of trying to make the lines come "almost together".

If you are just studying this subject for the first time you may not yet have encountered all the concepts that follow. Don't worry about that, just put it on the back burner.

An exercise that might be instructive is to compute the electric field strength in a region where a +5 Volt and -5 Volt surface are brought very close together (say, 1 mm). How does that compare to the breakdown voltage of various materials. What if you reduce the separation to a 0.1 mm? To 0.01 mm? To a micrometer? The form of the answer is $$ E \propto \frac{V_2 - V_1}{d}$$ for $d$ the separation distance. Notice that the field strength would grow without bound if you allowed the separation to go to zero: always a sign that you're in dicey territory.

These issue become critical in the design of compact capacitors.

Electric fields also carry energy. So, how much energy per unit volume is required to maintain two different potential surfaces very close together? (You'll want to make some simplifying assumptions about the geometry if you're going to calculate exactly, or go go with the form of the equations. The form of the answer here is $$U \propto E^2 \propto \frac{(\Delta V)^2}{d^2}$$ which may be what was meant by causing problems related to energy if you try to make them come all the way together: this diverges even faster than before.