First of all, you need to understand the difference between power and energy. Power over time is energy. For example, typical kettle (power is written on the label, let’s say it is 2kW), working constantly over one hour, will consume 2kWh of energy. Typical family home with gas or oil heating is using about 10kWh of electric energy per day.
Heating with electric energy is not the best idea as it is much more efficient to run heat pump compressor for heating (about 3 times more efficient than heating directly using electric heater or immersion element – depends on temperature difference of heat exchangers).
Let’s assume you have gas for heating and cooking, you are not wasting energy. All you need is 5kWh of energy per day which is 5kWh x 365days = 1825 kWh per year. South facing 2kW solar system will deliver just about that amount over the year, but the problem is that most of it during the summer. There may be a day where it will generate 8kWh a day and there could be a day when you generate not even 1 unit per day.
Next step is battery capacity given in Ah on the data label. In simple words typical 12V car battery with capacity of 100Ah should deliver current flow of 100Amps over 1h, or 10Amps over 10hours, or 1Amp over 100hours. There are loses involved but let assume it is a perfect battery ☺.
1Amp flowing from 12V battery can deliver even 12Watts of power! As stated above 1Amp can flow 100hours so that battery should deliver 12Watts over 100hours which is 1200Watt hours or 1.2kWh of energy. Now cut that half and you are about to get real values for a car battery which is not designed to store energy (car batteries are designed to start car so they can deliver high current).
Gel and AGM lead batteries are closer to these values but still, they are not designed to give 100% of its capacity while lithium batteries are closest to these values.