Monthly Anomaly Definition: The term anomaly means a departure from a reference value or long-term average. For example, a positive temperature anomaly indicates that the observed temperature was warmer than the reference value, while a negative anomaly indicates that the observed temperature was cooler than the reference value. The anomaly used in these plots uses the annual average monthly temperatures as the reference value subtracted from the monthly temperature of each month of the entire reanalysis period (e.g. 1980-2016).
(source https://www.ncdc.noaa.gov/monitoring-references/faq/anomalies.php)
Yearly Cycle Definition: The yearly cycle is the average of each month across the 35 years of the reanalyses. That is, January data displayed here is the average of all January data at the selected location.