Not only different voltage levels but different frequency levels as well (60-Hz in USA and 50-Hz in UK)
The exact rational thought behind this decision might be difficult to find. But as per legends and theories it was most probably the arbitrary/ random selection of voltage and frequency levels during the early days of electrification with USA using 110-V and UK and European countries using 220-V system.
Some of the main factors that triggered such selection were area demographics, manufacturer’s choice and geographical/ economical constraints.
During the early days electricity was generated, transmitted and distributed all in DC. In order to ensure public safety 110 Volt system was adopted in USA. The electrical supply system and other appliances were designed according to that voltage level at a fast pace in USA.
After the invention of induction machines especially Transformer, AC system found widespread usage in generation, transmission and distribution systems of electricity. We all know the inverse relation between voltage and current. Higher the voltage lesser will be the current and hence low cross sectional area conductor will be used to deliver the power.
After the breakthrough invention of Transformer many countries switched to higher voltage levels in order to transmit power at longer distance with less cost involved in the conductors employed for supply systems.
For USA, switching to this voltage level was not that easy and cost effective due the fact that the design of supply system plus large no. of public appliances being used at that time were compatible at 110-V. Thus altering the system was not a viable option. Hence they retained and proceeded with this secondary distribution voltage at 60-Hz.
UK and other European countries were among those countries that switched to higher voltage i.e. 220-V, 50-Hz scheme with relative ease (may be due to less infrastructure compatible with 110-V system compared to USA at that time).
Many of the Asian countries also use 220-V secondary distribution system probably because they remained under British influence and hence carried the same network topology.
Same is the case with frequency as USA and associated group of countries using 60-Hz and UK and related countries using 50-Hz system. The choice of frequency was more down to the monopoly of manufacturing companies in USA and Europe with former producing 60-Hz appliances and the latter going with 50-Hz devices.
These days both systems (220-V, 50-Hz and 110-V, 60-Hz) are happily operational and in full swing with not much hindrance faced by any of them.
Global standardization at common voltage and frequency levels is not a feasible option due to fairly large amount of cost involved because be it a change in frequency or a change in voltage, each one of them will require replacement of almost every single equipment involved in transmission and distribution systems of electricity.