Why do we have AC current from the mains but DC current on gadgets?

Electronic devices work off DC.

AC is easy to send over long distances because the voltage can be transformed up and down.
Many home appliances work off AC (cookers, microwave oven, washing machine,...)

AC is used for power transmission because you can use transformers with it. Transformers can supply the same amount of power while reducing the current. Reduced current results in reduced power loss during transmission.

DC is used for electronics because they use electricity for logic, not just power. If you tried to run a digital logic circuit with alternating current, you'd have to deal with the binary bits flashing back and forth between 0 and 1 with the cycle of the current. The mains voltage is also too high for transistors. Different transistors like different voltages, but usually around 1 to 5 volts. The answer about DC being used for portable electronics because it can be supplied by batteries is also good, but even non-portable electronics like desktop computers and video game consoles use DC.

With the expanding presence of DC, it would probably make sense for homes to be wired for DC. It would still be transmitted over the power lines as AC, but converted as it enters your home or somewhere in your neighborhood. The problem is that would require a change of standards, and standards are slow to change, because it's hard to accommodate both the old and new standard, and hard to get everybody to upgrade at the same time, particularly since it would be impractical to completely rewire an existing house.

Most electronic gadgets require D.C. to work.

However, in order to avoid massive losses when transferring power from the Power plant to the home A.C. is used.

At the home, the A.C. is converted to D.C. by using a transformer and rectifier; although, these days switch mode power supplies are used that do away with the isolation transformer.

DC is great at powering a single device but if it had to power something like Christmas Tree lights it loses it's power after supplying each light in the series so the last light in the strong might not light up at all AC overcomes this and supplies an equal voltage to all

DC is great at powering a single device but if it had to power something like Christmas Tree lights it loses it's power after supplying each light in the series so the last light in the strong might not light up at all AC overcomes this and supplies an equal voltage to all

There is no rule that AC and DC must be used compulsorily for any specific purpose. What you are stating above are merely observations about common uses of ac and dc.
Historically, Direct current (DC) was the first to be developed in form of cells. Only when scientists understood more about electricity and found ways to generate (by rotating conductors in magnetic fields), they found that this type of voltage is alternating.
This led to understanding the advantages of ac especially in generation and transmission. Which made it very popular.
But in electronic appliances, like radio, PC and so many small power applications the nature of problem is different. Here you need constant source to energize electronic components.
Conclusion
Choice of AC/DC is made only by the nature of application and ease of availability of specific source.
When you use solar cells, you directly get dc. But if you want to run fan from that source, you need to convert it to ac.

AC is easier to transport via power lines due to it's high efficiency and ease of use when step-up transformers and step-down transformers are needed. DC is storable and simple, therefore most useful for gadgets. Therefore mains power is AC for long distance transfers and batteries contain/produce DC because it is easy to store/unstore.
Also, if i am not mistaken, most gadgets actually use DC and mains AC is converted into DC in the power supply, at the Adapter.

Simple, DC is battery power and its portable otherwise you would need a very long and heavy duty extension cord so AC is used where mobility is not a concern like a building or home and can carry higher voltages and current