Astrophysicist and science communicator Neil deGrasse Tyson (and his dog) addressed this in a simple stroll down the beach.
In short, weather is what happens on any given day; climate is the mean of what happens over time. The climate of Florida, for example, is generally warm and humid, even during the winter. The weather at any given time in Florida may be sunny or rainy or cloudy or cooler or hotter (sometimes within a few minutes). The weather in New England may be sunny or rainy or colder or warmer at any given time as well, but it's a sure bet that on average it will be much colder in New England during the winter than in Florida. The former is weather, the latter is climate.
Another way to think about this is as the difference between trend and variation. The Tyson video above was inspired by an earlier animated video demonstrating the two terms.
In both videos the dog represents the ups and downs of yearly climate variation while the human's walking path is the trend. The trend is the average over time (more or less); the variation is the noisy short-term departure from that trend.
Which gets us to El Nino. There has been a lot of talk about the strong El Nino we've been experiencing. Climate deniers paid by lobbying groups have argued (falsely) that we wouldn't have set a new record without it. But actual climate scientists at NASA and NOAA have shown that 2015 would have set a new record anyway; the El Nino merely increased the magnitude of the record-breaking.
“2015 was remarkable even in the context of the ongoing El Niño,” said GISS Director Gavin Schmidt. “Last year’s temperatures had an assist from El Niño, but it is the cumulative effect of the long-term trend that has resulted in the record warming that we are seeing.”
El Nino, and its opposite counterpart La Nina, influence variation. As we've seen above, short-term phenomena have short-term affects on the year to year ups and downs in measurements like the global mean surface temperature (the most reported metric of climate change). Just like some days are sunny and others rainy, some years are warmer and others not as warm. That's the variation. That's the dog in the videos.
Trend is what happens over time. For the first 18 years of our lives the general trend is toward increasing height. For the last several decades, the general trend in climate has been toward increasing temperature.
That increasing trend is caused by increasing concentrations of CO2 and other greenhouse gases in the atmosphere. This CO2 comes from the burning of fossil fuels, which take carbon that has not been part of the natural cycle for millions of years and within a short period of time dumps it into the atmosphere and oceans. Since CO2 and other greenhouse gases control the temperature of the planet - keeping us about 30 degrees C more than it would be without them - adding more CO2 means more warming. Human activity has now added 40% more CO2 to the atmosphere (with even more in the oceans) than have been present in millions of years. The effects of this rise in CO2 and temperature are significant and a danger to humanity as we know it.
The bottom line is that there is the trend (CO2 and temperatures are rising over time) and variation (some years are warmer, some years are less warm). Deniers like to cherry pick "less warm" dates and create false narratives that ignore all the rest of the data. Actual climate scientists always look at the trends over time. The variations are important as well, mainly because they teach us how short-term phenomena like El Nino and La Nina influence the long-term trend. What we've learned from these variations is that CO2 is the primary driver of man-made global warming and the changes we've observed in our climate trends.