Conventional current and electron flow

​​In a nutshell

Conventional current is defined as current flowing from a positive terminal to a negative one while electrons flow the opposite way, from a negative terminal to a positive one. Electrolytes are liquids that can carry an electric current. 

Current in metals

The structure of a metal can be described as a lattice (crystal structure) of positive ions surrounded by free electrons. If you make one end of a metal wire positive and the other negative, these free electrons will start moving towards the positive terminal and will create an electric current. The greater the number of electrons moving through a point, the greater the current. 

Conventional current

The term conventional current was made long before the discovery of the electron and it is defined as current flowing from a positive terminal to a negative one. Due to its long history, conventional current is often used when working with circuits. Electrons flow the opposite way but this can still be visualized as a charge moving from the negative terminal to the positive, meaning that there is no issue with it.

Electrolytes

Since current is defined as the rate of flow of charge, it does not have to be created by flowing electrons; in liquids the charge carriers tend to be ions. Liquids that can carry charge are called electrolytes and they are mostly ionic solutions. An example is sea water, where salt (sodium chloride, $$NaCl$$​) is dissolved in water and separates into $$Na^+$$ (cations) and $$Cl^-$$ (anions).​

If you place a positive electrode (anode) and a negative electrode (cathode) in an ionic solution they will attract the oppositely charged ions towards each other. For example with salt water, the anode will attract the $$Cl^-$$ ions which will donate an electron while the cathode will attract the $$Na^+$$​ ions which will gain an electron, allowing the electrons to flow and create a circuit.

​​1. Anode 2. Electrolyte 3. Anions ($$Cl^-$$​) 4. Cathode 5. Beaker 6. Cations ($$Na^+$$​)